Uniform stabilization of a variable coefficient wave equation with nonlinear damping and acoustic boundary

ABSTRACT

In this paper we consider uniform stabilization of the wave equation with variable coefficients in a bounded domain. The nonlinear damping is put partly on the interior of the domain and partly on the acoustic boundary. Under some checkable conditions on the coefficients, the energy decay results are established by Riemannian geometry method.

Keywords:

• Riemannian geometry method
• variable coefficient
• acoustic boundary condition
• wave equation
• uniform stabilization

2010 Mathematics Subject Classifications:

• 35L05
• 35L20
• 35L70
• 35B35
• 35B40

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11901329] and the Natural Science Foundation of Shandong Province [grant number ZR2019BA022].